Scotland Yard has been ordered to review the disappearance of Madeleine McCann, after the child's mother appealed to the prime minister for help.

The Guardian understands that shortly after Kate McCann published an open letter in the Sun newspaper asking David Cameron to step in, Downing Street contacted the commissioner of the Metropolitan Police.

It was made clear that the Met should review the abduction of Madeleine, who at the age of three went missing from her parents' apartment four years ago in a holiday complex in Praia da Luz, Portugal.

Yard detectives will be working alongside the Portuguese police on the review of all the evidence in the case. But they will have to negotiate delicately around the primacy of the inquiry, which remains with the Portuguese detectives.

A statement from the Home Office announced the intervention and made clear that the government, not Scotland Yard, would be paying. "The government hopes that the MPS [Metropolitan Police Service] can bring a new perspective to the case and the Home Office will be providing the necessary financial support," the statement said.

In response, Kate and Gerry McCann thanked the government for their intervention. "We welcome the government's response," they said. "This is clearly a step in the right direction. We would like to thank Mr Cameron and the home secretary for committing such a significant resource as the Metropolitan police to begin this review process."

A Home Office spokesman said: "The government's primary concern has always been, and remains, the safe return of Madeleine. Although she disappeared in Portugal and the Portuguese retain the lead responsibility in the case, law enforcement agencies here have continued to follow up leads and pass information to the Portuguese authorities as appropriate.

"The prime minister and the home secretary have today agreed with [Commissioner] Sir Paul Stephenson that the Metropolitan police will bring its particular expertise to this case. Clearly, the detail of what that will entail will be a matter of operational judgment and it would not be appropriate to discuss at this stage."

Any inquiry into the disappearance of Madeleine is fraught with difficulties. Met detectives will fly to Portugal, though not imminently, to work with detectives there and review all the paperwork. But with the passage of time the chances of success are vastly reduced. The scene of the crime was never sealed off, and evidence is likely to have been contaminated or gone missing.

The Met face a huge challenge to find something within the paperwork that has been overlooked or misinterpreted. But they have no forensic evidence and no body to help their investigations.

Until today the Met were not going to be involved. The Guardian understood the likelihood of the Metropolitan Police Authority and the Mayor of London approving the expenditure on the case was very slim. After the open letter, the prime minister intervened, and crucially made clear the Home Office would pay for the investigation.

The Portuguese police inquiry was heavily criticised by the family, who themselves became official suspects.